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2 years ago

I need help with this

Mathematics

1 answer:

snow_lady [41]2 years ago

8 0

Answer:

x = 2 square roots of 2

Step-by-step explanation:

it is a 45-45-90 triangle and in that the two legs are equal to each other so both are 2 and then the hypotenuse is x times the square root of 2

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exis [7]

Answer:

Part 1) The length of the longest side of ∆ABC is 4 units

Part 2) The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

Step-by-step explanation:

Part 1) Find the length of the longest side of ∆ABC

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x ----> the length of the longest side of ∆ABC

y ----> the length of the longest side of ∆DEF

$z=\frac{x}{y}$

we have

$z=\frac{1}{10}$

$y=40\ units$

substitute

$\frac{1}{10}=\frac{x}{40}$

solve for x

$x=(40)\frac{1}{10}$

$x=4\ units$

therefore

The length of the longest side of ∆ABC is 4 units

Part 2) Find the ratio of the area of ∆ABC to the area of ∆DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of ∆ABC

y ----> the area of ∆DEF

$z^{2}=\frac{x}{y}$

we have

$z=\frac{1}{10}$

$z^2=(\frac{1}{10})^2$

$z^2=\frac{1}{100}$

therefore

The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

3 0

3 years ago

What is the value of x

pav-90 [236]

Let's start with triangle RST. This is a 30-60-90 triangle, which means it has the relationship x - x sqrt(3) - 2x.

If RS is 2 sqrt(3), then ST must be 2 and RT must be 4.

Triangle QRT is a 45-45-90 triangle, which means it has the relationship x - x - x sqrt(2).

If RT is 4, then RQ must also be 4.

Answer: x = 4

Hope this helps!

7 0

2 years ago

From a survey of 60 students attending a university, it was found that 9 were living off campus, 36 were undergraduates, and 3 w

lana66690 [7]

I think the question has to do with the number of students who are attending the university but is neither an undergraduate nor living off-campus. To help us solve this problem, we use the Venn diagram as shown in the picture. The intersection of the 2 circles would be 3 students. The students in the 'students living off-campus' circle would be 9 - 2 = 6, while the undergraduate students would be 36-3 = 33. The total number of students inside all the circles and outside the circles should sum up to 60 students.

6 + 3 + 33 + x = 60
x = 60 - 6 - 3 - 3
x = 18 students

Therefore, there are 18 students who are neither an undergraduate nor living off-campus

8 0

3 years ago

A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size of year-ending

Crank

Step-by-step explanation:

Consider the provided information.

The total number of students are: 24+26+21=71

He wants each team will have the same number of students between 5 and 9.

The number between 5 to 9 are 6, 7 and 8.

The number 71 is a prime number so we need to divide the 71 students in group so that minimum students left without team.

Dividing 6 students in each group.

Number of teams: $\frac{71}{6}$ = 11 teams and 5 students.

Dividing 7 students in each group.

Number of teams: $\frac{71}{7}$ = 10 teams and 1 students.

Dividing 8 students in each group.

Number of teams: $\frac{71}{8}$ = 8 teams and 7 students.

Thus, we can not divide 71 students into equal teams, but 70 divided by 7 gives the least students left out i.e 10 teams each with 7 students and only 1 student will remain at last.

6 0

3 years ago

A triangle has sides with lengths of 4 inches, 14 inches, and 17 inches. Is it a right triangle?

irga5000 [103]

Yes it is because 2 sides would be the legs while 1 side is the hyptonuese so in this case 4 is a leg and 14 and 17 is the hyptonuese

5 0

2 years ago